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"""Helper functions for axial attention."""
from operator import itemgetter
from typing import Callable, List, Tuple
from torch import nn, Tensor
def _map_el_ind(arr: Tensor, ind: int) -> List:
return list(map(itemgetter(ind), arr))
def _sort_indices(arr: Tensor) -> Tuple[List[int], List[int]]:
indices = [i for i in range(len(arr))]
arr = zip(arr, indices)
arr = sorted(arr)
return _map_el_ind(arr, 0), _map_el_ind(arr, 1)
def calculate_permutations(num_dims: int, emb_dim: int) -> List[List[int]]:
"""Returns permutations of tensor."""
total_dims = num_dims + 2
axial_dims = [i for i in range(1, total_dims) if i != emb_dim]
permutations = []
for axial_dim in axial_dims:
last_two_dims = [axial_dim, emb_dim]
dims_rest = set(range(0, total_dims)) - set(last_two_dims)
permutation = [*dims_rest, *last_two_dims]
permutations.append(permutation)
return permutations
class PermuteToForm(nn.Module):
"""Helper class for applying axial attention."""
def __init__(
self,
fn: Callable,
permutation: List[List[int]],
) -> None:
super().__init__()
self.fn = fn
self.permutation = permutation
_, self.inv_permutation = _sort_indices(self.permutation)
def forward(self, x: Tensor) -> Tensor:
"""Permutes tensor, applies axial attention, permutes tensor back."""
x = x.permute(*self.permutation).contiguous()
shape = x.shape
*_, t, d = shape
# Merge all but axial dimension
x = x.reshape(-1, t, d)
# Apply attention
x = self.fn(x)
# Restore original shape and permutation
x = x.reshape(*shape)
x = x.permute(*self.inv_permutation).contiguous()
return x
class Sequential(nn.Module):
"""Applies a list of paired functions to input."""
def __init__(self, fns: nn.ModuleList) -> None:
super().__init__()
self.fns = fns
def forward(self, x: Tensor) -> Tensor:
"""Applies blocks to input."""
for f, g in self.fns:
x = x + f(x)
x = x + g(x)
return x
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